Mohammed Abdulmalik, leader of the separatist movement STC, told AFP that in total there were seven airstrikes on a military base on Friday.
At least seven people have been killed and more than 20 injured, he said.
In December, the separatists carried out an offensive in Hadramawt and al-Mahra, two oil-rich provinces bordering Saudi Arabia and Oman.
A source close to the Saudi military confirmed to AFP that the Saudi-led coalition had carried out the airstrikes. The attacks will not stop until the separatists withdraw, according to the source.
According to the governor of Hadramawt, Salem al-Khanbashi, the ongoing effort to push back the separatists “should not be seen as a declaration of war” or an attempt to “escalate tensions.”
The goal is instead a “peaceful and systematic handover of military facilities,” he said in a speech on state television.
The events of recent weeks have increased fears of a larger conflict, and are seen as a sharp escalation in tensions between Saudi Arabia and the United Arab Emirates.
Saudi Arabia, which is allied with Yemen's internationally recognized government, has recently bombed arms shipments that it says were sent by Abu Dhabi to the separatists.
The STC and the government have previously been allies in the war against the Iran-backed Houthi movement.
